Scientia Iranica B (2014) 21(3), 609{619

Sharif University of TechnologyScientia Iranica

Transactions B: Mechanical Engineeringwww.scientiairanica.com

Prediction of all-steel CNG cylinder fracture underimpact using a damage mechanics approach

M. Yazdani Ariatapeh, M. Mashayekhi� and S. Ziaei-Rad

Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, P.O. Box 84156-83111, Iran.

Received 15 October 2012; received in revised form 5 August 2013; accepted 4 November 2013

KEYWORDSAll-steel CNGcylinder;Damage mechanics;Fracture;Impact.

Abstract. In this paper, a damage mechanics approach is used to investigate the e�ect ofcrash and damage caused by impact in a steel cylinder �lled by Compressed Natural Gas(CNG). The Canadian Standard Association (CSA) for CNG cylinders is used as a damagedetection criterion, and the cylinders' capability of reuse. The Johnson-Cook damagemodel is used to compute cylinder failures. Simulations are carried out in di�erent impactdirections, and the e�ect of cylinder internal pressure, collision velocity and fall heightare analyzed. Also, failure due to collisions in various situations is studied and discussed.Investigations for cases including crash and drop tests showed that the maximum damagein a cylinder is created in the case of normal impact and, by changing impact direction fromnormal to the side, the amount of damage will be decreased. Also, by eliminating failedelements and comparing the damage depth caused by collision using the CSA standard,it was observed that in most cases of normal accidents and drop tests, damaged cylinderslose their ability for reuse. However, in the case of side impact, the cylinder remains intactor can be reused after repair.© 2014 Sharif University of Technology. All rights reserved.

1. Introduction

High costs and the risk of empirical testing makethe use of numerical methods inevitable. From aneconomical viewpoint, natural gas is frugal fuel, withlow cost and abundant resources, and natural gascombustion pollution is lower than other common fossilfuels, such as gasoline and diesel. On the other hand, amajor issue in the use of natural gas fuel in cars is thestorage problem. Compressed natural gas cylinders areused for the storage of fuel at high pressure in cars withCNG. These cylinders are divided into four categoriesaccording to the manufacturer's material, including:all-metal, metal liner hoop wrapped, metal liner fully

*. Corresponding author. Tel.: +98 311 3915216;Fax: +98 311 3912628E-mail addresses: m.yazdaniariatape@me.iut.ac.ir (M.Yazdani Ariatapeh); mashayekhi@cc.iut.ac.ir (M.Mashayekhi); szrad@cc.iut.ac.ir (S. Ziaei-Rad)

wrapped and all-composite. All-steel cylinders withabout 92% percent usage are the most common typeof cylinder and the history of these cylinders goesback to the 1970s. Safety is one of the importantissues in the design and manufacture of such cylinders.All-metal cylinders use better known technology, withrespect to the other types of cylinder and, therefore,have more safety performance capability. According tothe importance of safety and to decrease the concernsof gas fuel car passengers, especially considering thee�ects of car accidents on CNG cylinders, it is necessaryto investigate cylinder impact conditions before use.Despite this, almost no studies have been reportedon the impact phenomenon of CNG cylinders. Somerelated studies have been quoted in the followingparagraphs.

In 1991, Becker et al. mentioned that the reactorpressure vessel/neutron shield tank assembly could beshipped safely without any risk to the public or theenvironment [1]. The reactor pressure vessel/neutron

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shield tank assembly was certi�ed by the U.S. Depart-ment of Energy as a type B package. A safety anal-ysis report for packaging was prepared in accordancewith the U.S. Department of Energy requirements toprovide the technical basis for the U.S. Departmentof Energy certi�cation. The reactor pressure ves-sel/neutron shield tank package is a monolithic struc-ture of lightweight concrete and steel. To substantiatemultidimensional inelastic analyses, a series of droptests was conducted on several benchmark models fromvarious heights. Technical evaluation and correlationof the test data were performed in conjunction withthe structural analysis and assessment of the package.Their research provides a comprehensive discussion onthe benchmark drop models and speci�c drop testsand also addresses the results obtained from comparingtechnical data with analytical data. The purpose of thebenchmark tests was to demonstrate that the results ofthe structural analyses of the package are a reasonablerepresentation of its real structural behavior.

In 1994, Rosenberg et al. conducted a series ofexperiments on high pressure vessels made of stainlesssteel in order to determine the critical pressures forcatastrophic failure under projectile impact [2]. Byusing gas dynamics calculations based on an idealgas equation of state expanding isothermally througha hole in the pressurized cylinder and adiabatic ex-pansion of a non-ideal gas, they found that there isconstant pressure within the vessel throughout thewhole process. In 2006, Nagel and Thambiratnam com-pared the energy absorption response of straight andtapered thin-walled rectangular tubes under obliqueimpact loading, for various load angles, impact velocityand tube dimensions [3]. All the computer modelingof the above-mentioned study was conducted usingthe nonlinear �nite element code ABAQUS/Explicitversion 6.3. It was found that the mean load and energyabsorption decrease signi�cantly as the angle of appliedload increases. Nevertheless, tapering a rectangulartube enhances its energy absorption capacity underoblique loading. The outcome of the study wasdesign information for the use of straight and taperedthin-walled rectangular tubes as energy absorbers inapplications where oblique impact loading is expected.According to various studies, cylinder internal pressure,projectile kinematic energy and the characteristics of acylinder are e�ective factors in the damage caused byimpact on under-pressure cylinders.

2. Problem analysis method

Ductile fracture criteria, such as the J-integral, thecohesive element method and the Gurson model, canbe used for the modeling of damage in cylinders.Due to uncoupled governing equations, these criteriacan be easily calibrated and implemented in a �nite

element code. Needing few coe�cients and by applyingaccurate calibration, they are appropriate candidatesfor use in the simulation of impact problems. Thisis why they have been widely used in industrialpractices [4]. All the above damage models assumethat the damage model is uncoupled with the materialconstitutive equations. It means that the fracturecriteria are checked at each step outside the loop ofstress and strain calculations. When an accumulateddamage indicator reaches a critical value in an element,it fails and completely loses its load-carrying capability.

Among damage models based on ductile fracturecriteria, the Johnson-Cook (JC) model, which is for-mulated in the space of stress triaxiality and equivalentplastic strain, is capable of predicting realistic fracturepatterns and, at the same time, correct residual veloc-ities. Thus, this model is suitable for the predictionof fracture caused by impact problems [5]. Johnsonand Cook developed a constitutive model to describematerial properties under dynamic loading [6]. Thevon Mises yield criteria with the associated ow ruleis used in this material model. Its isotropic hardeninglaw includes the e�ects of strain rates and temperaturerise. In conjunction with their material constitutiveequation, Johnson and Cook also proposed a fracturecriterion for dynamic loading problems. Similar to thematerial constitutive model, the fracture strain wasassumed to be a function of stress triaxiality, strainrates, and temperature in an uncoupled form, de�nedby:

��=[A+B"npl]�1+C ln

�_"pl_"0

���1��T�T0

Tm�T0

�q�;(1)

"f =hD1 +D2exp

�D3

�h��

�i �1 +D4 ln

�_"pl_"0

���1 +D5

T � T0

Tm � T0

�; (2)

where �� is the equivalent stress; �h is hydrostatic pres-sure; "pl is the e�ective plastic strain; _"pl and _"0 are thecurrent and reference strain rates, respectively; Tm andT0 are the melting and room temperature, respectively;and A, B, n, C, q and D1,..., D5 are material constantswhich need to be calibrated by experimental data.This model accounts for isotropic strain hardening,strain rate hardening and temperature softening in anuncoupled form.

The �rst term in the brackets in the right handside of Eq. (2) has the same form as that proposedby Hancock and Mackenzie [8], and represents thefracture characteristics of a specimen under quasi-staticloading conditions at room temperature. Since anexponential function was employed in the �rst term,Johnson and Cook implied that the fracture locus

M. Yazdani Ariatapeh et al./Scientia Iranica, Transactions B: Mechanical Engineering 21 (2014) 609{619 611

could be represented by one continuous curve in theentire range, and the fracture strain decreases with theincreasing stress triaxiality. In a general case, stresstriaxiality is not constant but varies during a loadingprocess. The stress triaxiality, de�ned as the ratioof the hydrostatic pressure to the equivalent stress,is commonly introduced in the literature to representthe stress state mentioned in Eq. (2). Note thathydrostatic pressure is the �rst invariant of the stresstensor, and the von Mises stress is the square root ofthe second invariant. Both invariants are independentof a coordinate system, and, thus, suitable for largeplastic deformation. Impact problems involve largeplastic deformation, high strain rates, and elevatedtemperature. Johnson and Cook assumed that damageaccumulates in a linear way [7], i.e:

D =Z "pl

0

1"fd"pl: (3)

An element fails when D reaches unity, i.e. Dcr = 1.Due to high strain rates, heat generated by a largeportion of plastic energy would not have su�cient timeto escape to surrounding materials, which leads totemperature rise. Both strain rates and temperatureclearly have an e�ect on the fracture characteristics of aspecimen. According to the features that were countedon for Johnson-Cook's model and its availability inmost �nite element codes, it is used in the presentpaper.

3. Problem analysis

In this section, the modeling and analysis of CNG cylin-ders are presented and the results of the simulations areexplained in detail.

3.1. Preliminary cylinder simulationA 60-lit cylinder manufactured by the Faber Companyin Italy is considered. The length of the cylindricalsection is 668 mm. The inner and the outer diametersof the cylindrical section are 318 mm and 301:8 mm, re-spectively. The dimensions of the two end hemisphereused in the simulations are given in Figure 1. Thecylinder is made of 4340 alloy steel, Johnson-Cook'smaterial and damage model constants for this steel arelisted in Table 1 [7].

Figure 1. Scheme of the Faber all-steel cylinder in termsof mm [10].

The simulations are performed with the �nite ele-ment software ABAQUS/Explicit [4], and the Johnson-Cook plasticity model and the Johnson-Cook damagemodel of ABAQUS/Explicit are used to describe theplastic constitutive material behavior and the damageinitiation and propagation. For collision cases, sideand normal directions, and for drop tests, side, oblique(45�) and normal directions, are considered. The CSAstandard for a CNG cylinder is used to evaluate theimpact damage and the ability to reuse the cylinderafter collision. This association lists general guidelinesfor the value of the damage in the CNG cylinder inthree levels. The levels are as follows [9].

- Level 1: Any scratch, gouge, or abrasion with adamage depth of less than, or equal to, 0.010 inch(0:25 mm). First level damage occurring on a cylinderis acceptable and it does not need to be repaired.

- Level 2: Any scratch, gouge, or abrasion witha damage depth of 0.011 to 0.050 inch (0.27 to1.27 mm). Second level damage requires rework(either in the �eld or by the manufacturer), a morethorough evaluation or destruction of the cylinder,depending on severity.

- Level 3: Any scratch, gouge, or abrasion with adamage depth greater than 0.050 inch (1.27 mm).Third level damage is severe enough that the cylindercannot be repaired and must be destroyed. All �reand chemical damage is Level 3, if it does not washo� [9].

According to the above levels, �ne meshes were

Table 1. Material and damage model constants for 4340 alloy steel [7].

E (GPa) � � (kg/m3) Tm(K) T0(K) Cy(j/kg.K)

200 0.29 7830 1793 293 477

�(K�1) A (MPa) B (MPa) n C m

0.000032 792 510 0.26 0.014 1.03

_"0(S�1) D1 D2 D3 D4 D5

1 0.05 3.44 -2.12 0.002 0.061

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used up to the depth of 1:27 mm from the outersurface of the cylinder wall. Also, areas that aredirectly under impact have �ner meshes where fractureis expected to occur. Relatively coarse meshes wereused in the other part of the cylinder for increasingthe speed of computing. Eight-node, linear brickelements with reduced integration were used. Failedelements were removed to illustrate the formation andgrowth of cracks. The kinematic contact constraint wasprescribed at the impact interface, which allows theprojectile to elastically rebound from the rigid wall atthe end of the impact process. The friction coe�cientbetween the front surface of the cylinder and the rigidwalls is assumed to be 0.1. The duration of 20 ms isconsidered for all simulations. The results indicate thatthe damage during this period reaches a constant value.

3.2. Collision simulation of CNG cylindersIn this section, analysis of CNG cylinders under frontand side collisions is investigated. The idea is to �ndout the e�ect collision direction has on the extentof damage in the cylinder. Due to the symmetry,only one-half of the cylinders was considered and thesymmetric boundary conditions were applied at theplane of symmetry.

According to Figures 2 to 5, two cubes-shapedrigid surfaces are considered. One of them is thecylinder support during the accident, while the otheris used as the impactor. To investigate the e�ect ofinternal pressure and the impactor collision velocity onthe amount of damage to the cylinder, several caseswere considered. The cases are listed in Table 2.

Pressure was uniformly applied to the inner sur-face of the cylinder. It should be mentioned that aspeed of 120 km/h is the maximum velocity limit onhighways.

Comparing the amount of damage on both sidesof the cylinder shows that in the side collision, someareas in connection with the cylinder and the headsof the cylinder are damaged more than other parts(Figure 3). However, in a front impact, the middleparts of the heads of the cylinder have been damagedmore than other areas and are, thus, considered criticalareas (Figure 5).

Figure 2. Deformed model of the cylinder after sidecollision.

Figure 3. Critical area after side collision.

Figure 4. Deformed model of the cylinder after frontcollision.

Figure 5. Critical area after front collision.

Table 2. Case studies for evaluation of damage on the CNG cylinder under collision.

Case studies Pressure(bar)

Collision velocity(km/h)

Collision direction

Case 1 200 120 SideCase 2 200 120 FrontCase 3 200 180 SideCase 4 200 180 FrontCase 5 50 180 SideCase 6 50 180 Front

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By removing damaged elements from the dam-aged areas, in Figures 6 to 8, it is observed that fora side collision under working pressure (200 bars) anddi�erent velocities (i.e. cases 1 and 3), the depth ofthe damage in the cylinder wall is lower than the limitsexpressed in the CSA standard. Therefore, the cylindercan be used, if it is repaired again. However, undera pressure of 50 bars and at a velocity of 180 km/h(cases 5 and 6), the depth of the damage exceedsthe acceptable amount, and the cylinder cannot bereused. In all states of front collision (cases 2, 4 and 6),the depth of damage on the cylinder wall exceeds theacceptable amount of damage and the cylinder cannotbe reused. For cases under the pressure of 50 bars, thelevel of indentation depth is greater than similar casesunder working pressure. This shows that by decreasingcylinder internal pressure, the amount of damage willbe increased.

Figures 9 and 10 show that, initially, the damagein all cases has grown rapidly and, after a short time, it

Figure 6. Damaged critical area in the collision for (a)case 1, and (b) case 2.

Figure 7. Damaged critical area in the collision for (a)case 3, and (b) case 4.

becomes at. The results also indicate that for impactsin a front direction, the amount of damage was abouttwice in comparison with impacts in a side directionunder the same conditions. Consequently, the numberof omitted elements for impacts in a front directionis more. Also, it can be concluded that in cylinderswith low pressure and higher velocity, the amountof accumulated damage for each speci�c direction ismore.

Comparing the history of equivalent plastic strainbetween critical points of collision in Figures 11 and 12,it shows that this quantity follows a trend very similarto the damage. Again, in the front direction, lesspressure and higher colliding velocity creates moreplastic strain. Figures 13 and 14 show the history ofstress triaxiality for critical area in various directionsof collision. A stress triaxiality of less than �0:5 isobserved in most damaged areas. In the beginning thecollision process, stress triaxiality rapidly decreases inthe critical region for graphs corresponding to frontcollision. This indicates that for cases of higher

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Figure 8. Damaged critical area in the collision for (a)case 5, and (b) case 6.

Figure 9. Damage growth rate at the critical damagedarea for cases 1 to 4.

pressure, the bending is of more dominance in theseareas.

Figure 15 shows a mesh study for cases 3 and 4for a typical point in the critical area and for a pointat a depth of 1:27 mm (maximum depth of damage).

Figure 10. Damage growth rate at the critical damagedarea for cases 3 to 6.

Figure 11. History of the equivalent plastic strain at thecritical damaged area for cases 1 to 4.

The closeness of results to each other indicates that theobtained response does not depend on the mesh quality.

3.3. Drop test simulation of CNG cylindersIn this section, the analysis of the CNG cylinder for adrop test in side, oblique (45�) and normal directionsis presented. According to Figures 16 to 19, in�nite element models, the rigid surface of the cube-shaped cylinder has been considered as the collidingsurface. In addition to di�erent internal pressure, 25and 6 m height of drop for each simulation directionhave been applied as the initial velocity to the cylin-der.

Figure 20 shows the critical area of the cylinderfor side and oblique drop tests. Similar results were

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Figure 12. History of the equivalent plastic strain at thecritical damaged area for cases 3 to 6.

Figure 13. History stress triaxiality at the criticaldamaged area for cases 1 to 4.

obtained for the other side and oblique drop tests,which are not reported here for the sake of brevity.The results show that for all cases of side and obliquedrop tests, the depth of damage does not go beyondthe critical limit, and the cylinder can be used withoutany need for repair. It is noteworthy that by decreasingthe internal pressure, the damage grows; however, itsextent does not lead to the removal of any element fromthe cylinder.

According to Figures 21 and 22, when a cylinderwith 200 bars pressure is dropped from di�erent heightsalong a normal direction, the extent of the damage issomehow that after repair, the cylinder has the abilityto be reused. Under conditions where the cylinder hasan internal pressure of 50 bars and has fallen from a

Figure 14. History of stress triaxiality at the criticaldamaged area for cases 3 to 6.

Figure 15. Damage rate in the collision for cases 3 and 4(at 5 and 10 nodes from the outer surface of cylinder wall).

Figure 16. The deformed cylinder model after side droptest.

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Figure 17. Critical area after side drop test.

Figure 18. The deformed cylinder model and criticalarea after oblique drop test.

Figure 19. The deformed cylinder model and criticalarea after normal drop test.

height of 25 meters, the depth of the damage has gonebeyond the critical value and the cylinder is not usable.

Figures 23 and 24 show the variation of damageversus time. The graphs indicate that the damage hasgrown rapidly and eventually reaches a constant value.Also, the amount of accumulated damage in a dropfrom a normal direction is more than in the others.By changing the angle of collision from the front tothe side direction, the value of the damage is reduced.The amount of damage in normal drop increases morerapidly compared to the drop in other directions. Theslope of the damage curves decrease by reducing theangle of collision. It can be concluded that by reducing

Figure 20. The critical area of the cylinder for (a) theside drop, and (b) oblique drop.

the pressure or increasing the height of the drop, thedamage will be increased in all directions.

According to Figures 25 and 26, the equivalentplastic strain in the drop test follows the same trendas the damage growth. Here, for normal drop, lesspressure and higher fall, higher plastic strain occurs.According to Figures 27 and 28, stress triaxiality isnegative most of the time, which indicates that thedamaged area is primarily under pressure. The dropin the stress triaxiality diagrams in the damaged areais a�ected by the pressure of bending, which is dueto hitting the outer wall of the cylinder. It can beconcluded that for a particular damaged area alonga speci�c direction, at higher velocity and pressure,the drop in the graph of its corresponding triaxialityis more.

4. Conclusions

This paper examines the e�ect of direction and collisionvelocity, internal pressure and the height of fall onthe damage in all-steel CNG cylinders using a damage

M. Yazdani Ariatapeh et al./Scientia Iranica, Transactions B: Mechanical Engineering 21 (2014) 609{619 617

Figure 21. The critical area of the cylinder in normaldrop for pressure of 200 bars: (a) Height of 6 m; and (b)height of 25 m.

Figure 22. The critical area of the cylinder in normaldrop for pressure of 50 bars and the height of 25 m.

mechanics approach. Two series of simulations werecarried out on the CNG cylinders, namely, collision anddrop test simulations. Reviewing the diagrams showsthe maximum amount of damage occurred in drop froma normal direction, and by changing the drop directionfrom normal to side, the value and extent of damagewill be reduced. With the removal of damaged elementsand by comparing the depth of the damage in collisionwith the CSA standard, it was observed that in most

Figure 23. Damage growth rate in a typical point atdamaged area (internal pressure of 200 bars).

Figure 24. Damage growth rate in a typical point atdamaged area (height = 25 m).

Figure 25. History of equivalent plastic strain at atypical point of damaged area (internal pressure= 200 bars).

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Figure 26. History of equivalent plastic strain at atypical point of damaged area (height = 25 m).

Figure 27. History of stress triaxiality at a typical pointof damaged area (internal pressure = 200 bars).

Figure 28. History of stress triaxiality at a typical pointof damaged area (height = 25 m).

collision cases, and in a normal drop, the cylinder losesits ability to function.

In terms of side collision, the cylinder remainswith no defect, and after repairing, it has the abilityfor reuse.

Results of simulation also showed that in all typesof impact in cylinders with lower internal pressure thedamage grows more than cylinders with higher internalpressure.

The results also revealed that in both side andfront collisions, the cylinder's rear wall and the fronthead of the cylinder have more damage and are criticalareas.

For a speci�c impact direction, by increasing col-lision velocity and the altitude of fall, or by decreasingcylinder pressure, the damage will also increase.

References

1. Becker, D.L., Burgess, D.M. and Lindquist, M.R.\Drop testing conducted to benchmark the shipping-port reactor pressure vessel package safety analysis",Nucl. Eng. Des., 130, pp. 133-145 (1991).

2. Rosenberg, Z., Mironi, J., Cohen, A. and Levy, P.\On the catastrophic failure of high-pressure vessels byprojectile impact", Int. J. Impact Eng., 15, pp. 827-831 (1994).

3. Nagel, G.M. and Thambiratnam, D.P. \Dynamic sim-ulation and energy absorption of tapered thin walledtubes under oblique impact loading", Int. J. ImpactEng., 32, pp. 1595-1620 (2006).

4. Teng, X. \High velocity impact fracture", PhD Thesis,Massachusetts Institute of Technology (2004).

5. Teng, X. and Wierzbicki, T. \Evaluation of six frac-ture models in high velocity perforation", Eng. Fract.Mech., 73, pp. 1653-1678 (2006).

6. Johnson, G.R. and Cook, W.H. \A constitutive modeland data for metals subjected to large strains, highstrain rates and high temperatures", in: Proceedingsof the Seventh International Symposium on Ballistics.,Hague, Netherlands, pp. 541-47 (1983).

7. Johnson, G.R. and Cook, W.H. \Fracture characteris-tics of three metals subjected to various strains, strainrates, temperatures and pressures", Eng. Fract. Mech.,21(1), pp. 31-48 (1985).

8. Hancock, J.W. and Mackenzie, A.C. \On the mecha-nisms of ductile failure in high strength steels subjectedto multi-axial stress-states", J. Mech. Phys. Solids.,24, pp. 147-169 (1976).

9. CSA America Inc. \CNG fuel system inspector studyguide", National Energy Technology Laboratory, U.S.Department of Energy, DE-FC26-05NT42608 (2008).

10. T Ribarits, S.G. \Assessment of inspection criteriaand techniques for recerti�cation of natural gas vehicle(NGV) storage cylinders", M.Sc. Thesis, MechanicalEngineering Department, University of British Colom-bia (1983).

M. Yazdani Ariatapeh et al./Scientia Iranica, Transactions B: Mechanical Engineering 21 (2014) 609{619 619

Biographies

Mohammad Yazdani Ariatapeh received BS andMS degrees in Mechanical Engineering from SharifUniversity of Technology, Iran, in 2008, and IsfahanUniversity of Technology, Iran, in 2011, respectively.His research interests include solid design damageand fracture mechanics, �nite element method andadvanced design by computer.

Mohammad Mashayekhi received his PhD degreein Mechanical Engineering, in 2006, from IsfahanUniversity of Technology, Iran, where he is currentlyAssociate Professor of Mechanical Engineering. His

research interests include damage mechanics, fracturemechanics, �nite element method.

Saeed Ziaei-Rad received BS and MS degrees in Me-chanical Engineering from Isfahan University of Tech-nology, Isfahan, Iran in 1988 and 1990, respectively,and his PhD degree from the Department of MechanicalEngineering at Imperial College of Science and Tech-nology, London, UK, in 1997. He is currently Professorand faculty member in the Mechanical EngineeringDepartment of Isfahan University of Technology, Iran.He has many papers published in international journalsand presented at conferences in his academic �elds ofinterest.